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Harrison W.A. — Elementary electronic structure
Harrison W.A. — Elementary electronic structure

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Название: Elementary electronic structure

Автор: Harrison W.A.


This text presents an account of analytic electronic structure, to be distinguished from computational electronic structure. Both are based upon a one-electron approximation, local-density theory, and the determination of the quantum-mechanical electronic states. They both seek to predict the properties of the resulting solids, or molecules on the basis of these states.In the computational mode, the minimum number of approximations are used, and numerical solutions are sought. Here we seek instead to focus on the most important aspects of the solution, making what approximations are necessary in order to proceed analytically and obtain formulae for the properties. This reducing of the problem to basics is almost always less accurate that the computational solution, but has the advantage that it displays the dependence of any property on the parameters of the system. It gives us an understanding of the property in a sense that a numerical solution, or a direct measurement, cannot.

Язык: en

Рубрика: Физика/

Серия: Библиотека «Математическое просвещение»

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 819

Добавлена в каталог: 19.03.2006

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Предметный указатель
$k\dot p$ method      230
$\mathrm{Li_2}$      11—16 51pr 52pr
$\mathrm{O_2}$      52pr
$\mathrm{SiO}_2$      see “Silicon dioxide”
A15 structure      592
Abruptness of repulsion      89 117
Absorbtion threshold      216ff 221
Absorption of light      see “Optical absorption”
Accommodation      556
Acoustic vibrational modes      124 (see also “Vibrational frequencies”)
Actinides      see also “f-shell metals”
Actinides, cohesive energy      618 619
Actinides, compounds      682ff
Actinides, crystal structure      620 624
Actinides, volume-dependent energy      619ff
Adsorption, atoms on semiconductors      749ff
Aliased interactions      724
Alkali halides      see “Ionic crystals”
Alkali halides, Susceptibility      382ff
Alkali metals, high pressure transition      576 (see also “Simple metals”)
Alloys, energy bands      304
Alloys, semiconductors      294ff
Alloys, simple metals      513ff
Alloys, structure      298
Alloys, transition metals      578ff
Alumina, $\mathrm{Al_2O_3}$      430
Americium      637 (see also “ f-shell metals”)
Anderson localization      625ff
Angular forces      104 131ff
Angular forces, hydrides      782
Angular forces, metals      496
Angular forces, silicon dioxide      411ff
Antibonding bands      183ff
Antibonding states, $Li_2$ states      13
Antibonding states, semiconductors      63
Antiferromagnetism, chromium      552
Antiferromagnetism, cuprates      708ff
Antiferromagnetism, f-shell metals      638
Antiferromagnetism, transition metals in general      590
Antisite defect      312 313
Antisymmetry of electron states      450
Atomic electron states      5
Atomic electron states, core states      8
Atomic electron states, term values, plot      7
Atomic electron states, term values, table for d-states      645
Atomic electron states, term values, table for f-states      683
Atomic electron states, term values, table for s, p-states      9
Atomic Sphere Approximation      554ff 565
Atomic sphere radius, simple metals, table      436
Atomic sphere radius, transition metals, table      539
Atomic Surface Method      531 556ff 672ff
Auger processes      321
Average lattice      298 304
Axial ratio, hep structures      437 488 586
Axial ratio, hep structures, table      438
Baldereschi points      348ff
Ball-and-stick model for semiconductors      137 138
Band gap      see “Energy gap”
Band iine-ups at interfaces      741ff
Band structure      see “Energy band”
Band width, Atomic Surface Method      558
Band width, d-bands      549 560
Band width, f-shell metals      603
Band width, narrowing in cuprates      706
Band width, second moment      560ff
Band-structure energy, simple metals      483
Bechstedt form for overlap repulsion      67 68 80 90
Beta cristobalite      400 422
Beta-eucryptite      430
Binding energy of solids      see “Cohesive energy”
Bloch sums      18 56 345
Body-centered-cubic structure      183 437
Bom Model, ionic crystals      330 339ff 367 716
Bom-Oppenheimer Approximation      207
Bond energy      see “Cohesive energy”
Bond length, $\mathrm{Zn_3P_2}$      758
Bond length, boron      760
Bond length, dependence upon coordination      99 100
Bond length, effect of metallization      85
Bond length, graphite, prediction for      106pr
Bond length, inert-gas solids      768
Bond length, ionic crystals      361ff
Bond length, rare-earth nitrides      682
Bond length, simple metals      see “Nearest-neighbor distance”
Bond length, table, ionic crystals      330
Bond length, table, semiconductors      60 211 216
Bond length, transition metals      see “Atomic sphere radius”
Bond length, transition-metal compounds      660 661
Bond length, trends in semiconductors      85ff
Bond order, transition-metal alloys      582
Bond-charge model      132
Bond-Orbital Approximation, diatomic molecule      28
Bond-Orbital Approximation, mathematics of      74
Bond-Orbital Approximation, semiconductors      70ff
Bond-Orbital Approximation, silicon dioxide      407 411ff
Bond-Orbital Approximation, support for, from moments      98
Bonding states, bonding bands      183ff
Bonding states, dipoles      143 144
Bonding states, floating      777
Bonding states, graphite      106pr
Bonding states, in $Li_2$      13
Bonding states, metallization      75ff
Bonding states, multicenter      754ff
Bonding states, pseudopotential theory      508ff
Bonding states, three-center (delta)      759
Bonding unit      308
Bonding unit, boron      759
Bonding unit, impurity states      307ff
Bonding unit, multicenter bonds      754ff
Bonding unit, silicon dioxide      400 401
Boron      759ff
Bowing of energy bands      305
Bragg reflection      465
Bravais lattice      56
Brillouin Zone, crystals      180ff
Brillouin Zone, cuprates      706
Brillouin Zone, extended and reduced      472
Brillouin Zone, one dimension      18
Bucky balls      773—775
Bulk modulus, $\mathrm{Zn_3P_2}$      758
Bulk modulus, boron      760
Bulk modulus, fiuorite      352pr
Bulk modulus, ionic crystals      351 352pr 363ff
Bulk modulus, rare earths      617 618
Bulk modulus, ruthenium dioxide      688
Bulk modulus, semiconductors      87 108ff
Bulk modulus, silicon dioxide      416
Bulk modulus, simple metals      443 494 496
Bulk modulus, transition metals      574 575
Bulk modulus, transition-metal compounds      667
c/a ratio, hep structures      437 488 586
c/a ratio, hep structures, table      438
Calcium      see “Simple metals”
Calcium fluoride      see “Fiuorite”
Calcium, structure determination      578
Carbyne, elasticity, metallization      141pr
Carbyne, energy bands      213pr
Carbyne, vibration spectrum      134ff
Cauchy relations      367 375 496 497ff
Cellular method      554
Central-hydride molecules      781ff
Cerium      603 608 611ff 622 635ff
Cerium, nitride      681
Cesium-chloride structure      329
Cesium-chloride structure, overlap repulsion in      360
Charge-density wave      708
Chemical grip      368 700
Chromium, electronic structure      550ff
Cohesive energy, $\mathrm{Zn_3P_2}$      758
Cohesive energy, actinide compounds      687
Cohesive energy, actinides      618 619
Cohesive energy, boron      760
Cohesive energy, Coulomb corrections, semiconductors      82ff
Cohesive energy, dependence upon polarity      82
Cohesive energy, elemental semiconductor, formula      80
Cohesive energy, elements, table      21
Cohesive energy, inert-gas solids      768
Cohesive energy, ionic crystals      336 363
Cohesive energy, ionic crystals, fiuorite      352pr 353pr
Cohesive energy, ionic crystals, table, divalent      338
Cohesive energy, ionic crystals, table, monovalent      337
Cohesive energy, nitrogen molecule      27
Cohesive energy, one-dimensional chain      20
Cohesive energy, perovskites      694
Cohesive energy, rare earths      614ff
Cohesive energy, semiconductors      70ff
Cohesive energy, semiconductors, table      80
Cohesive energy, silicon dioxide      406ff
Cohesive energy, simple metals      440ff
Cohesive energy, transition metals      569ff
Cohesive energy, transition-metal compounds      647 667 678pr
Complementarity      556
Compounds, f-shell-metals      680ff (see also “Ionic crystals” “Semiconductors”
Conduction band      64
Conduction band, ordering of levels at r      176 177
Configuration interaction      83
Core radius      39 (see also “Empty-core pseudopotentials”)
Core states      8
Correlated states      84 599
Correlated states, criteria for      601 631ff
Correlated states, cuprates      709ff
Correlated states, formation of local moments      625ff
Correlated states, role in lattice spacing      622
Correlation energy      83 207
Correlation energy, band narrowing in cuprates      707
Correlation energy, effects on magnetism      591
Correlation energy, f-shell and transition metals      593ff
Correlation energy, free-electron gas      451
Correlation energy, photothresholds and work functions      727
Correlation energy, transition-metal compounds      668
Correlation energy, Van-der-Waals interaction      765ff 768
Coulomb effects      see also “ Madelung energy”
Coulomb effects, band gaps      206ff 326 341 423
Coulomb effects, band narrowing in cuprates      707
Coulomb effects, cohesion of semiconductors      82ff
Coulomb effects, d-state shifts in transition metals      561ff
Coulomb effects, d-state shifts in transition metals, from atomic calculations      561
Coulomb effects, impurities in semiconductors      745
Coulomb effects, in compounds      659ff 691 695 705
Coulomb effects, ionic crystals, bonding      372ff
Coulomb effects, ionic crystals, elastic constants      375ff
Coulomb effects, Madelung potential      82
Coulomb effects, photothresholds and work functions      50 727
Coulomb effects, surfaces      716
Coulomb repulsion, U      10
Coulomb repulsion, U, d-states      46 561
Coulomb repulsion, U, d-states, in f-shell metals      610ff
Coulomb repulsion, U, d-states, table      539
Coulomb repulsion, U, f-states      607ff
Coulomb repulsion, U, sp-atoms, table      9
Coulomb repulsion, U, total energy in semiconductors      69
Coupling between electronic states      see “Matrix elements”
Covalency      63
Covalent energy, $sp^3$-hybrids      29
Covalent energy, f-shell-metal compounds      680
Covalent energy, from second moment, $V_2^*$      98
Covalent energy, ionic crystals      344 352pr 359
Covalent energy, perovskites      695
Covalent energy, pseudopotentials, related to      512 513
Covalent energy, silicon dioxide      404
Covalent energy, sp-hybrids, defined      59ff
Covalent energy, sp-hybrids, defined, table      60
Covalent energy, transition-metal compounds      657
Crystal structure, actinides      620 624
Crystal structure, alkali metals under pressure      576
Crystal structure, beta cristobalite      400
Crystal structure, body-centered-cubic      437
Crystal structure, cesium chloride      329
Crystal structure, cuprates      706
Crystal structure, density of states role      577 57
Crystal structure, face-centered-cubic      54ff 434ff
Crystal structure, fluorite ($\mathrm{CaF_2}$)      351
Crystal structure, graphite      105
Crystal structure, hexagonal close-packed      437
Crystal structure, ionic crystals      329
Crystal structure, packing fractions      481pr
Crystal structure, perovskite      693
Crystal structure, prediction for graphite      104
Crystal structure, pyrite      430
Crystal structure, rare earths      618
Crystal structure, rock-salt      329
Crystal structure, rutile      688
Crystal structure, S, Se, and Te      752
Crystal structure, semiconductors      53ff
Crystal structure, semiconductors, prediction      99ff
Crystal structure, silicon dioxide      400ff
Crystal structure, simple metals      435ff
Crystal structure, simple metals, prediction      488
Crystal structure, transition metals      576ff
Crystal structure, wurtzite      57
Crystal structure, zincblende      53ff
Crystallographic directions      55
Cuprates      49 704ff
Curie temperature      590
Current operator and continuity      739
d-states      6 534ff
d-states, Coulomb shifts in compounds      659ff 705
d-states, Coulomb shifts in transition metals      561
d-states, coupling between      542
d-states, coupling between, Slater — Koster tables      546
d-states, energy bands      45 545ff 592pr
d-states, energy bands, $\mathrm{Nb_3Sn}$      592pr
d-states, energy bands, band widths, table      539
d-states, f-shell metals      610ff
d-states, localization of      43 530
d-states, overlap repulsion      568 569 582
d-states, radius, $r_d$      43 531
d-states, radius, $r_d$, definition      537
d-states, radius, $r_d$, obtaining from Atomic Surface Method      558
d-states, radius, $r_d$, table      539 674
d-states, self-consistent shifts of $\varepsilon_d$      45 561 659ff 705
d-states, semiconductors, role in      672ff
Dangling hybrids, or bonds      314
Debye — Huckel screening      289
Debye — Waller factor      478
Deep levels      309ff
Defects, antisites      312 313
Defects, interstitials in semiconductors      317
Defects, vacancies in semiconductors      314ff
Deformation potentials      254ff 270 292pr
Deformation potentials, strain-layer superlattices      745ff
Dehybridization energy, silicon dioxide      413
Density of states, chromium nitride      651
Density of states, misleading for some problems      704
Density of states, semiconductors      245ff
Density of states, transition metals      552ff
Density of states, wavenumber space      182
Density-functional theory      5 664ff
Diagonalization of matrices      18 73ff 95
Diamagnetism, semiconductors      159
dielectric constant      see “Dielectric susceptibility”
Dielectric constant, defined      147
Dielectric constant, static      165ff
Dielectric constant, table for semiconductors      211
Dielectric function      289 469
Dielectric function, Lindhard or Hartree      462 485
Dielectric properties, ionic crystals      379ff
Dielectric properties, semiconductors      143ff
Dielectric susceptibility, inert-gas solids      764ff
Dielectric susceptibility, ionic crystals, local-field effects      387ff
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